Best and simple data structure

I would think it would be simpler to use an un-nested dictionary with two-character keys.

myDictionary.add("AA", 4)

Use a two dimensional array and create a mapping for your alphabet as an enumeration that will also serve as an index into the arrays:

public enum AlphaBet
{
   A = 0,
   R = 1,
   ...
}

// Init the array
int[][] scores = ...;

int score = scores[AlphaBet.A][AlphaBet.N]; // score = -2